In this study, quaternary-ammonium-functionalized metal–organic frameworks (MOFs) Et-N-Cu(BDC-NH2)(DMF), were prepared, characterized, and applied for the highly effective removal of metal cyanide complexes, including Pd(CN)42−, Co(CN)63−, and Fe(CN)63−. Batch studies were carried out, and the maximum adsorption capacities of Pd(II), Co(III), and Fe(III) reached 172.9, 101.0, and 102.6, respectively. Adsorption was rapid, and equilibrium was established within 30 min. Et-N-Cu(BDC-NH2)(DMF) exhibited high thermal and chemical stability. Furthermore, absorbed Pd(CN)42− was selectively recovered by two-step elution. First, Co(CN)63− and Fe(CN)63− were eluted with a 1.5 mol L−1 KCl solution. Elution rates of Co(CN)63− and Fe(CN)63− were greater than 98.0%, whereas the elution percentage of Pd(CN)42− was less than 2.0%. Second, >97.0% Pd(CN)42− on the loaded MOFs was eluted using a 2.0 mol L−1 KI solution. The recovery rate of Pd(CN)42− was greater than 91.0% after five testing cycles. Adsorption isotherms, kinetics models, and adsorption thermodynamics of Pd(CN)42− on Et-N-Cu(BDC-NH2) (DMF) were also systematically investigated. The Et-N-Cu(BDC-NH2) (DMF) absorbent exhibited a rapid, excellent ability for the adsorption of metal cyanide complexes.